11.2 A Primitiveren met de kettingregel

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11.2 A Primitiveren met de kettingregel

Bepaal de afgeleide

f (x) = \sqrt ​ 4 x - 5 ​ ​ ​

f (x) = \sqrt ​ 4 x - 5 ​ ​ ​

f^{​' ​ ​} (x) = \frac{​ 1 ​ ​}{​ 2 \sqrt ​ 4 x - 5 ​ ​ ​ ​} \cdot 4

f^{​' ​ ​} (x) = \frac{​ 2 ​ ​}{​ \sqrt ​ 4 x - 5 ​ ​ ​ ​}

Primitiveren met kettingregel

f (x) = \sqrt ​ 4 x - 5 ​ ​ ​

Primitiveren met kettingregel

f (x) = \sqrt ​ 4 x - 5 ​ ​ ​

f (x) = (4 x - 5)^{​ \frac{​ 1 ​ ​}{​ 2 ​} ​ ​}

Primitiveren met kettingregel

f (x) = \sqrt ​ 4 x - 5 ​ ​ ​

f (x) = (4 x - 5)^{​ \frac{​ 1 ​ ​}{​ 2 ​} ​ ​}

F (x) = \frac{​ 1 ​ ​}{​ 1 \frac{​ 1 ​ ​}{​ 2 ​} ​} \cdot (4 x - 5)^{​ 1 \frac{​ 1 ​ ​}{​ 2 ​} ​ ​} \cdot \frac{​ 1 ​ ​}{​ 4 ​} + C

Primitiveren met kettingregel

f (x) = \sqrt ​ 4 x - 5 ​ ​ ​

f (x) = (4 x - 5)^{​ \frac{​ 1 ​ ​}{​ 2 ​} ​ ​}

F (x) = \frac{​ 1 ​ ​}{​ 1 \frac{​ 1 ​ ​}{​ 2 ​} ​} \cdot (4 x - 5)^{​ 1 \frac{​ 1 ​ ​}{​ 2 ​} ​ ​} \cdot \frac{​ 1 ​ ​}{​ 4 ​} + C

F (x) = \frac{​ 1 ​ ​}{​ 6 ​} \cdot (4 x - 5)^{​ 1 \frac{​ 1 ​ ​}{​ 2 ​} ​ ​} + C

Primitiveren met kettingregel

f (x) = \sqrt ​ 4 x - 5 ​ ​ ​

f (x) = (4 x - 5)^{​ \frac{​ 1 ​ ​}{​ 2 ​} ​ ​}

F (x) = \frac{​ 1 ​ ​}{​ 6 ​} \cdot (4 x - 5)^{​ 1 \frac{​ 1 ​ ​}{​ 2 ​} ​ ​} + C

F (x) = \frac{​ 1 ​ ​}{​ 6 ​} (4 x - 5) \sqrt ​ 4 x - 5 ​ ​ ​ + C

Bepaal de primitieven:

f (x) = (2 x - 4)^{​ 3 ​ ​} + sin (5 x)

f (x) = (2 x - 4)^{​ 3 ​ ​} + sin (5 x)

F (x) = \frac{​ 1 ​ ​}{​ 4 ​} (2 x - 4)^{​ 4 ​ ​} \cdot \frac{​ 1 ​ ​}{​ 2 ​} - cos (5 x) \cdot \frac{​ 1 ​ ​}{​ 5 ​} + C

F (x) = \frac{​ 1 ​ ​}{​ 8 ​} (2 x - 4)^{​ 4 ​ ​} - \frac{​ 1 ​ ​}{​ 5 ​} c o s (5 x) + C